On Egoroff's theorems on fuzzy measure spaces

Abstract

In this paper, we show that Egoroff's theorem, which is well known in classical measure theory, remains valid for a fuzzy measure without any additional condition. Previous results obtained by Wang Zhenyuan and others are improved. Egoroff's theorem on fuzzy measure spaces is formulated in full generality. Taylor's theorem which concerns convergence almost everywhere in classical measure theory is also extended to fuzzy measure spaces.